Part I: Modeling of Hormone Feedback Networks

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Part I Modeling of Hormone Feedback Networks

• Understanding Endocrine Oscillations

Raina Robeva Sweet Briar College
June 14, 2009 BERE Symposium, Izmir, Turkey
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1947 DRS. J.D. Green G.W. Harris Hypothesized
that certain substances

• 1) Are synthesized and released by hypothalamic
  neurons
• 2) Are transported by hypothalamic-hypophyseal
  portal circulation to the anterior pituitary
  gland
• 3) Influence the secretion of pituitary hormones

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• 1971-72 The Discovery of Gonadotropin
• Releasing Hormone (GnRH)
• A 10-amino acid peptide capable of stimulating
  the release of LH and FSH
• Concentrated, purified and characterized from
  hypothalamic extracts from the
• Pig (Matsuo and colleagues, BBRC 1971)
• Sheep (Burgus and colleagues, PNAS 1972)

Schally Guillemin
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• Studies in the Rhesus Monkey from the
  Knobils Laboratory(1970-1980)
• Lesioning of the medial basal hypothalamus
  abolishes gonadotropin secretion
• Administration of GnRH in a continuous manner
  fails to restore gonadotropin secretion
• Administration of GnRH in a pulsatile manner
  restores gonadotropin secretion
• Administration of antibody to GnRH abolishes
  gonadotropin secretion

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Pulsatile Secretion of Hormones
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LH Pulsatility During the Human Menstrual Cycle

• Pulse frequency (/24 hours)
• Early follicular 14-24
• Late follicular 17-29
• Mid-luteal 4-16

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The pattern of delivery is crucial to hormone
action

• The action of many hormones is impaired if
  pulsatility is lost
• Moreover, if a hormone is delivered continuously
  the effect could be negative
• Therefore, understanding the forces driving
  hormone oscillations is particularly important in
  medicine and biology

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Challenges Two Competing Processes-- Secretion
and Ongoing Elimination
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Challenges

• Data points are very expensive to collect and
  process
• The typical cost of a clinical laboratory assay
  is approximately 50 per sample
• The Figure has 144 data points and each was
  assayed twice
• The cost for the assays alone was approximately
  15,000
• This does not include the clinical staff time,
  payments to the volunteer.

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Pulsatility Software
Michael Johnson, Ph.D Department of Internal
Medicine Division of Endocrinology and
Metabolism University of Virginia
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Method Output
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Question

• With so many factors present in the hormone
  network, what would be a good approach to the
  problem?
• How can a good mathematical model be developed?

good (relatively) simple useful
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Wiring Diagrams

• Rectangles used to denote system variables,
  e.g. GH, GHRH, SRIF
• Lines indicate causality
• Line labels () excitatory action
• (-) inhibitory action
• Triangles indicate delay
• Ovals to indicate elimination

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Feedback and Delayscan cause oscillations
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Growth Hormone

• The Growth Hormone (GH) is secreted from the
  pituitary gland under the control of substances
  released from the hypothalamus

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Individual representative male rat GH profiles
Lanzi R. Tannenbaum, G. Time Course and
Mechanism of Growth Hormones Negative Feedback
Effect on its Own Spontaneous Release.
Endocrinology, Vol. 130, 2 (1992), 780-788.
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Major factors controlling GH release

• An universally accepted understanding is that
  pulsatile GH secretion is regulated by two major
  factors released from the hypothalamus
• (GH stimulator) GH-releasing hormone (GHRH)
• (GH inhibitor) somatostatin (SRIF)
• Numerous other substances could impact the GH
  output. However, they are considered not to be
  responsible for the typical GH pulsatility

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Elements of the GH network

• GH, GHRH, SRIF, and the interconnections between
  them form the core GH network
• Question Could this simplified network alone
  explain the typical rat GH rhythm?

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Consensus GH Feedback Network
()

(
-
)

SRIF

GHRH

()

(

-

)

GH

D



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Rate of change of hormone concentration

• Elimination
• Source controlled by other hormones

Secretion
Elimination
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Physiological Meaning of the Parameters
Elimination
Secretion
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Equivalent Formulation as a Convolution Integral
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Steps of the Proof
1. Show that   2. Show that   3. Show that
  4. Finally, use that
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Modeling the Control of Secretion

• Hill functions

n5 and T50
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Hormone A depends on Hormone B
B
A
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Hormone A depends on Hormone B
B stimulates the secretion of A
()
B
A
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Hormone A depends on Hormone B
B inhibits the secretion of A
(-)
B
A
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Hormone A depends on Hormone B
B inhibits the secretion of A with a delay of D
hours
(-)
B
A
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Example
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When hormones B and C affect the secretion of A
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The control function as a combination of Hill
functions

• If B and C both stimulate A
• Simultaneously
• Independently

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Consensus GH Feedback Network
()

(
-
)

SRIF

GHRH

Model output
()

(

-

)

GH

D


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Individual representative male rat GH profiles
Lanzi R. Tannenbaum, G. Time Course and
Mechanism of Growth Hormones Negative Feedback
Effect on its Own Spontaneous Release.
Endocrinology, Vol. 130, 2 (1992), 780-788.
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Presumed GH Feedback Network
Model output
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How can a feedback model help?

• It provides a possible physiological explanation
  of the behavior of complex endocrine systems.
• Could be used for testing various hypotheses. It
  could quickly provide answers to non-trivial
  questions of the type what if, or it could
  simulate the eventual effect of the simultaneous
  actions of several factors.
• It could be very helpful in the process of
  designing of new experiments, some of which could
  be very sophisticated and difficult to perform in
  the lab.
• The interpretation of the experimental results
  can be significantly simplified.

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• William Evans, MD, Ph.D.
• Leon Farhy, Ph.D
• Department of Internal Medicine
• Division of Endocrinology and Metabolism
• University of Virginia

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Discussion

• Control functions accounting for the effect of
  multiple hormones
• Delay
• Why Hill functions?
• Sensitivity Analysis